# How Much CP Will I Get From a Chaos Legion Pack?

Introduction
So we all know that Chaos Legion is coming out. It's an exciting time, with the upcoming new cards and new format, which will (hopefully) make the game more accessible. But the question we all must ask ourselves is this: do we buy the packs or do we buy individual cards? Well, I'm not here to answer that question, but rather help you answer it for yourself by laying out some statistics I found by simulating the opening of 1,000,000 packs.

Explanation of my Model
My model uses the given drop rates of common, rare, epic, and legendary cards (both gold and regular) and simulates the creation of 1,000,000 packs. These drop rates are taken from https://peakmonsters.com/packs. Then, if the pack only contains commons, it replaces a common with a rare.

Important Note: This will lead to an increase in rares and a decrease in commons as compared to the given numbers. I am not sure how exactly the game guarantees a pack to have at least 1 rare or better, so if someone tells me how I can improve my model.

Model 1: Without Potions
DO NOT OPEN YOUR PACK WITHOUT POTIONS. That was my takeaway from this model. It is a really bad idea. With that in mind, I'll walk you through the stats.

Theoretical average CP: 119
Model's average: 121.76 (as I said, it overestimates rares ever so slightly)
Median: 40
Mode: 40
Min: 40
Max: 15030

This means over 50% of the data is clustered at 40. Of the 1 million packs this simulated, over 500,000 were worth 40 (506,886 to be exact).

Here is a histogram of the data. The x axis is CP, the y axis is count.

There is a 29.3% chance that you get a pack with CP at or above the expected average of 119.

There is a 6.3% chance that you get a pack with CP at or above 300. That means that there is only a 6.3% chance that the pack you open is worth more (in terms of airdrop points) than the unopened pack. But when it is more than 300, there's a good chance it is worth at least 515 (97.66%).

Takeaways:

1. Compare this to model 2, which used potions. PLEASE USE POTIONS.
2. It is unlikely you will get the average, or beat the average. But when you do, it will be very worth your while.

Model 2: With Both Potions
Okay. Once again. Please use potions. If you take nothing else away from this, I hope I've explained this enough.

Theoretical average CP: 190.88
Model's average: 193.3 (again, it overestimates rares ever so slightly)
Median: 55
Mode: 40
Min: 40
Max: 25630

A look at two histograms:
All data

Only packs under 550 CP

There is a 38.9% chance you get a pack over 119 CP.

There is a 15.9% chance you get a pack over the expected average of 190 CP.

There is a 12.4% chance you get a pack over the pack's airdrop value of 300, and a 97.7% chance that a pack over 300 is over 515 as well.

Value
How much should a pack be worth? At the moment, the cheapest card by CP per dollar is 33.333 CP per dollar. That means each CP is worth approximately 3 cents. At an average of 190, the going rate of a pack should be at least \$5.70. Keep in mind, this is assuming that all cards you pull from a pack go at the lowest rate on the market. That is highly unlikely, so they should likely be more, even if just for their CP.

Questions
I hope this was interesting and helpful for you! Please let me know if you have any questions that you'd like me to explore, or if you have a way to improve my model. Or even if you just want clarification!

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This is a fantastic report. Important too! Keeping the airdrop points in mind is critical. Nice work!

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Thank you!

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This is a good post, and will be helpful to a lot of folks!

Below are some comments for future posts.

You x- and y-axes would benefit from some labels.

A log-log plot would also be helpful here, as it will reign in the crazy differences in scale on the opposite sides of the graph.

You also don't really need to simulate: each card has a well-defined probability mass function, and the sum of PMFs is pretty straightforward.

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I thought it would be useful for finding the median and also just modeling for specific levels of CP (ie over 300 has these odds). I appreciate the tips though, and definitely agree I should've included axes.

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I have a beginner's doubt.
How many potions do I need per pack? 5 of both?
Are you counting the potions in your Model 2 to determine the cost of the pack?

This info es amazing!

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5 per pack, and yes I am assuming potions in determining the price of a pack. Thank you!

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(Edited)

This is a very great report and and how you break them down is awesome, I have planned my game plan when the 8th comes, thanks for this !

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Thank you again for the support!

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